Cluster and level algorithm
Resources, operations and buffers are connected with each other with loads and flows. An operation has a collection of loads and flows. Each flow establishes a connection with a buffer, and each load a connection with a resource. The entities thus constitute a network graph. In this network context we define clusters and level as follows.
A cluster is a set of connected entities. When a network path across loads and flows exists between 2 entities they belong to the same cluster. When no such path exists they are effectively situated in independent partitions of the network.
Clusters allow us to group entities and are very useful in multithreaded environment: since the clusters are completely independent we can use different threads to solve each cluster as a separate subproblem.
Material flows in the network have a direction. This creates a sense of direction in our network which is expressed by the level concept. An operation consumes and produces material, as defined by the flow entities (aka bill of material or recipe). In this context the level is a number that is defined such that the level of a consumed material buffer is always higher than the level of the produced material buffer. The demand is normally (but not exclusively!) placed on the material buffers with level 0, and the level number increases as we recurse through the different levels in the bill of material. Raw materials have the highest level number.
The level and cluster number are helpful for the various solver algorithms. They provide valuable information about the structure of the network.
The algorithm used to compute the level and cluster information is based on a walk through the network: We select an unmarked operation and recurse through the loads and flows to find all connected entities, updating the cluster and level information as we progress.
For efficiency, the algorithm is implemented as a lazy function, i.e. the information is only computed when the user is retrieving the value of a level or cluster field. The algorithm is not incremental (yet), but computes the information for the complete network in a single pass: a change to a single entity will trigger re-computation of all level and cluster information for all entities.
The pseudo-code of the algorithm is as follows:
// Initialisation Lock the function Reset the level and cluster to -1 on all resources, operations and buffers Reset the total number of clusters // Main loop Loop through all operations // Check the operation If the operation has no producing flow Activate the level computation If the operation isn’t part of a cluster yet Activate the cluster computation Increment the cluster counter If both cluster and level computation are inactive, move on to the next operation // Recursively process the operation stack Push the current operation on the recursion stack, with level 0 or -1 Loop until the stack is empty Pop an operation from the recursion stack Pop the value of cur_level from the stack // Detect loops in the network structure If the operation was already visited in the recursion loop Move on to the next operation Loop through the sub operations and super operations If their level is less than the current level Push sub operation on the stack, with the same level as the current operation Set the level and cluster fields Else if cluster is not set yet Push sub operation on the stack, with -1 as the level Set the cluster field Loop through all loads of the operation If level search is active and the resource level is less than the level of the current operation Update the level of the resource If the cluster of the resource is not set yet Set the cluster of the resource Loop through all operations that are loading the resource If operation cluster isn’t set yet Push the operation on the stack, level -1 Set the cluster of the operation Loop through all flows of the current operation If this is a consuming flow and level_search is active and the buffer’s level is less than the current level +1 Level recursion is required If level recursion is required or the cluster of the buffer is not set yet Set the cluster of the buffer Loop through all flows connected to the buffer If it is a consuming flow and level search recursion was enabled If operation level < level + 1 else if operation cluster isn’t set yet Push the operation on the stack, level -1 Set the buffer level to level + 1 else if operation cluster is not set yet Push the operation on the stack, level -1 Set the cluster of the operation // Catch buffers missed by the main loop Loop through all buffers which don’t have any flow at all. Increment the total number of clusters Set the cluster number to the new cluster // Catch resources missed by the main loop Loop through all resources which don’t have any load at all. Increment the total number of clusters Set the cluster number to the new cluster // Finalization Unlock the function